This invention relates to a display system for a three-dimensional graphic in which shading is made and more particularly to a display system having a reflection light intensity control device that is suitable to display a shaded object on the basis of the reflection model of light.
It is well known to vary the reflection light intensity or shade at each of the points of a displayed graphic in order to display a three-dimensional graphic on a two-dimensional display device so that the displayed graphic has a three-dimensional effect. One of the model equations for computing the reflection light intensity is disclosed in the reference "Fundamentals of Interactive Computer Graphics" Addison Wesely Publishing Company, 1982, pp. 575-578. As seen from this reference, the intensity (reflection light intensity) of reflection light that reaches the viewpoint from a certain point (reflecting point) of a certain surface (reflection surface) is written as: ##EQU1## where I.sub.a : intensity of ambient light at a reflecting point
I.sub.p : intensity of a point light source PA0 n: specular reflection factor PA0 N: normalized normal vector to a reflection surface PA0 L: normalized vector to the point light source PA0 R: normalized vector in the direction of specular reflection PA0 V: normalized vector in the direction of the viewpoint PA0 r: distance from the reflecting point to the viewpoint (depth) PA0 K.sub.a : ambient-light-reflection coefficient PA0 K.sub.d : diffuse-reflection coefficient PA0 K.sub.s : specular-reflection coefficient PA0 k: constant
FIG. 2 illustrate several vectors included in Equation (1).
The values of the variables other than K.sub.a, K.sub.d, K.sub.s and k vary depending upon the positions of the individual points on the reflection surface. Each of K.sub.a, K.sub.d, K.sub.s, I.sub.a and I.sub.p can be separated into a red component (R), green component (G) and blue component (B) and Equation (1) is valid for each color component, which is also true of the Equations offered hereinbelow. K.sub.a, K.sub.d, K.sub.s, and n depend on the material of the reflecting surface but do not depend on the position of the individual reflecting point on the reflection surface. Since the dot product (R.multidot.V) at the third term in Equation (1) can be replaced by the dot product (N.multidot.H) of N and the normalized vectors H in the middle direction between the light source and the viewpoint (i.e. the direction of the sum of L and V) Equation (1) can be transformed into ##EQU2## Further, Equation (2) can be regarded as a sum of the following two terms: ##EQU3## In Equation (3), I.sub.a K.sub.a is a reflecting light component by the ambient light, and the remainder is a diffuse reflecting light component by the light from the light source. Thus, I'.sub.ad represents the diffuse reflecting light component as a whole. On the other hand, I.sub.s ' in Equation (4) is a specular reflecting light component. Further, it will be understood that both those two components are functions of a depth r (distance between the viewpoint and the reflecting point) and a normalized normal vector N to the reflection surface.
In the display device for two-dimensionally displaying a three-dimensional graphic, it is necessary to compute the reflection light intensity I of each of the points (reflecting points) on the three dimensional graphic, corresponding to each of the pixels on the two-dimensional graphic. If Equation (2) is used for this purpose, however, the computing is very time-consuming since Equation (2) includes several multiplications and divisions. In the technique disclosed on pages 543 and 544 of the above reference, the reflection light intensity I varied at each point is displayed using only the depth r. In this technique, however, some graphics cannot be displayed with a sufficient three-dimensional effect since different surfaces having the same depth r carry the same reflection light intensity. Further, in the graphic shading device disclosed in Japanese Patent Application No. 59-223922 that was filed before this application and was laid open after the Conventional priority date of this application, it was proposed to compute the reflection light intensity I at each reflecting point, assuming that the depth r in Equation (2) is constant, by the following equation ##EQU4## where C is constant.
If the reflection light intensity varied at each point is indicated by the reflection light intensity only in the direction of the reflection surface, graphics are displayed with the same reflection light intensity, when a plurality of graphics to be displayed are in the same direction or form the same angle with the direction of the light source or viewpoint, and it becomes impossible to recognize boundaries of graphics and it may provide spoiled three-dimensional effect, if they are contiguous to each other.
Further, in accordance with the use of the display device, it is desired that the reflection light intensity variation be exaggerated depending upon the difference or it is exaggerated depending upon the difference of the direction of the normal line. The prior art, however, can not implement this.